Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = 1000001000;
const long long INFL = 2000000000000001000;
int solve();
int main() {
  srand(2317);
  cout.precision(10);
  cout.setf(ios::fixed);
  int tn = 1;
  for (int i = 0; i < tn; ++i) solve();
}
const int maxn = 100100;
const int maxd = 17;
const int BOUND = 10;
const int ROOT = 0;
vector<int> g[maxn];
vector<int> combine(const vector<int> &a, const vector<int> &b) {
  vector<int> res(((int)(a).size()) + ((int)(b).size()));
  res.erase(set_union(a.begin(), a.end(), b.begin(), b.end(), res.begin()),
            res.end());
  if (((int)(res).size()) > BOUND) res.resize(BOUND);
  return res;
}
int p[maxd][maxn];
vector<int> P[maxd][maxn];
int in[maxn], out[maxn];
int timer = 0;
vector<int> who[maxn];
void dfs(int u, int prev) {
  in[u] = timer++;
  p[0][u] = prev;
  P[0][u] = who[prev];
  for (int v : g[u])
    if (v != prev) dfs(v, u);
  out[u] = timer;
}
inline bool isPrev(int u, int v) { return in[u] <= in[v] && out[v] <= out[u]; }
vector<int> calc(int u, int v) {
  vector<int> res = combine(who[u], who[v]);
  for (int deg = maxd - 1; deg >= 0; --deg)
    if (!isPrev(p[deg][u], v)) {
      res = combine(res, P[deg][u]);
      u = p[deg][u];
    }
  if (!isPrev(u, v)) {
    int deg = 0;
    res = combine(res, P[deg][u]);
    u = p[deg][u];
  }
  for (int deg = maxd - 1; deg >= 0; --deg)
    if (!isPrev(p[deg][v], u)) {
      res = combine(res, P[deg][v]);
      v = p[deg][v];
    }
  if (!isPrev(v, u)) v = p[0][v];
  assert(v == u);
  return res;
}
int solve() {
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = 0; i < int(n - 1); ++i) {
    int u, v;
    scanf("%d%d", &u, &v), --u, --v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  for (int i = 0; i < int(m); ++i) {
    int where;
    scanf("%d", &where), --where;
    vector<int> cur(1, i);
    who[where] = combine(who[where], cur);
  }
  dfs(ROOT, ROOT);
  for (int deg = 0; deg < int(maxd - 1); ++deg)
    for (int u = 0; u < int(maxn); ++u) {
      p[deg + 1][u] = p[deg][p[deg][u]];
      P[deg + 1][u] = combine(P[deg][u], P[deg][p[deg][u]]);
    }
  for (int i = 0; i < int(q); ++i) {
    int u, v, a;
    scanf("%d%d%d", &u, &v, &a), --u, --v;
    vector<int> res = calc(u, v);
    if (((int)(res).size()) > a) res.resize(a);
    cout << ((int)(res).size());
    for (int x : res) cout << ' ' << x + 1;
    cout << '\n';
  }
  return 0;
}